Effect of viscoelasticity on the analysis of single-molecule force spectroscopy on live cells

Single-molecule force spectroscopy is used to probe the kinetics of receptor-ligand bonds by applying mechanical forces to an intermediate media on which the molecules reside. When this intermediate media is a live cell, the viscoelastic properties can affect the calculation of rate constants. We theoretically investigate the effect of media viscoelasticity on the common assumption that the bond force is equal to the instantaneous applied force. Dynamic force spectroscopy is simulated between two cells of varying micromechanical properties adhered by a single bond with a constant kinetic off-rate. We show that cell and microvilli deformation, and hydrodynamic drag contribute to bond forces that can be 28-90% lower than the applied force for loading rates of 10(3)-10(7) pN/s, resulting in longer bond lifetimes. These longer bond lifetimes are not caused by changes in bond kinetics; rather, they are due to the mechanical response of the intermediate media on which the bonds reside. Under the assumption that the instantaneous bond force is equal to the applied force--thereby ignoring viscoelasticity--leads to 14-39% error in the determination of off-rates. We present an approach that incorporates viscoelastic properties in calculating the instantaneous bond force and kinetic dissociation parameter of the intermolecular bond.     

The NTA-His6 bond is strong enough for AFM single-molecular recognition studies

There is a need in current atomic force microscopy (AFM) molecular recognition studies for generic methods for the stable, functional attachment of proteins on tips and solid supports. In the last few years, the site-directed nitrilotriacetic acid (NTA)-polyhistidine (Hisn) system has been increasingly used towards this goal. Yet, a crucial question in this context is whether the NTA-Hisn bond is sufficiently strong for ensuring stable protein immobilization during force spectroscopy measurements. Here, we measured the forces between AFM tips modified with NTA-terminated alkanethiols and solid supports functionalized with His6-Gly-Cys peptides in the presence of Ni2+. The force histogram obtained at a loading rate of 6600 pN s(-1) showed three maxima at rupture forces of 153 +/- 57 pN, 316 +/- 50 pN and 468 +/- 44 pN, that we attribute primarily to monovalent and multivalent interactions between a single His6 moiety and one, two and three NTA groups, respectively. The measured forces are well above the 50-100 pN unbinding forces typically observed by AFM for receptor-ligand pairs. The plot of adhesion force versus log (loading rate) revealed a linear regime, from which we deduced a kinetic off-rate constant of dissociation, k(off) approximately 0.07 s(-1). This value is in the range of that estimated for the multivalent interaction involving two NTA, using fluorescence measurements, and may account for an increased binding stability of the NTA-His6 bond. We conclude that the NTA-His6 system is a powerful, well-suited platform for the stable, oriented immobilization of proteins in AFM single-molecule studies.     

How the biotin-streptavidin interaction was made even stronger: investigation via crystallography and a chimaeric tetramer

The interaction between SA (streptavidin) and biotin is one of the strongest non-covalent interactions in Nature. SA is a widely used tool and a paradigm for protein-ligand interactions. We previously developed a SA mutant, termed Tr (traptavidin), possessing a 10-fold lower off-rate for biotin, with increased mechanical and thermal stability. In the present study, we determined the crystal structures of apo-Tr and biotin-Tr at 1.5 ? resolution. In apo-SA the loop (L3/4), near biotin's valeryl tail, is typically disordered and open, but closes upon biotin binding. In contrast, L3/4 was shut in both apo-Tr and biotin-Tr. The reduced flexibility of L3/4 and decreased conformational change on biotin binding provide an explanation for Tr's reduced biotin off- and on-rates. L3/4 includes Ser45, which forms a hydrogen bond to biotin consistently in Tr, but erratically in SA. Reduced breakage of the biotin-Ser45 hydrogen bond in Tr is likely to inhibit the initiating event in biotin's dissociation pathway. We generated a Tr with a single biotin-binding site rather than four, which showed a simi-larly low off-rate, demonstrating that Tr's low off-rate was governed by intrasubunit effects. Understanding the structural features of this tenacious interaction may assist the design of even stronger affinity tags and inhibitors.     

Single molecule characterization of P-selectin/ligand binding

P-selectin expressed on activated platelets and vascular endothelium mediates adhesive interactions to polymorphonuclear leukocytes (PMNs) and colon carcinomas critical to the processes of inflammation and blood-borne metastasis, respectively. How the overall adhesiveness (i.e. the avidity) of receptor/ligand interactions is controlled by the affinity of the individual receptors to single ligands is not well understood. Using single molecule force spectroscopy, we probed in situ both the tensile strength and off-rate of single P-selectin molecules binding to single ligands on intact human PMNs and metastatic colon carcinomas and compared them to the overall avidity of these cells for P-selectin substrates. The use of intact cells rather than purified proteins ensures the proper orientation and preserves post-translational modifications of the P-selectin ligands. The P-selectin/PSGL-1 interaction on PMNs was able to withstand forces up to 175 pN and had an unstressed off-rate of 0.20 s(-1). The tensile strength of P-selectin binding to a novel O-linked, sialylated protease-sensitive ligand on LS174T colon carcinomas approached 125 pN, whereas the unstressed off-rate was 2.78 s(-1). Monte Carlo simulations of receptor/ligand bond rupture under constant loading rate for both P-selectin/PSGL-1 and P-selectin/LS174T ligand binding give distributions and mean rupture forces that are in accord with experimental data. The pronounced differences in the affinity for P-selectin/ligand binding provide a mechanistic basis for the differential abilities of PMNs and carcinomas to roll on P-selectin substrates under blood flow conditions and underline the requirement for single molecule affinity measurements.     

Displacement smoothing for the precise MRI-based measurement of strain in soft biological tissues

Displacement and strain are fundamental quantities that describe the normal and pathological mechanical function of soft biological materials. Non-invasive imaging techniques, including displacement-encoded magnetic resonance imaging (MRI), enable the direct calculation of biomaterial displacements during the application of extrinsic mechanical forces. However, because strain is derived from measured MRI-based displacements, data processing must be accomplished to minimise the propagation and amplification of errors. Here, we evaluate smoothing methods (including averaging filters, splines, finite impulse response filters and wavelets) that enable the calculation of strain in biomaterials from MRI-based displacements for minimal error, defined in terms of bias and precision. Displacement and strain precisions were improved using all smoothing methods studied. Precision generally increased with the number of smoothing iterations (i.e. repeated applications) of a chosen smoothing method. The bias depended on the smoothing method and tended to increase with the number of smoothing iterations. A Gaussian filter characterised complex and heterogeneous strain fields with maximum precision and minimum bias. The results suggest that the optimal choice of smoothing method to compute strain for a given biomaterial or tissue application depends on a careful consideration of trade-offs between the improved precision (with increased data smoothing) and the trending increase in bias.     

Monitoring receptor-ligand interactions between surfaces by thermal fluctuations

We describe a new method for determining receptor-ligand association/dissociation events across the interface of two surfaces (two-dimensional binding) by monitoring abrupt decrease/resumption in thermal fluctuations of a biomembrane force probe. Our method has been validated by rigorous control experiments and kinetic experiments. We show that cellular on-rate of association can be measured by analysis of intervals from a dissociation event to the next association event (waiting times). Similarly, off-rate of molecular dissociation can be measured by analysis of intervals from an association event to the next dissociation event (bond lifetimes). Different types of molecular bonds could be distinguished by different levels of reduction in thermal fluctuations. This novel method provides a powerful tool to study cell adhesion and signaling mediated by single or multiple receptor-ligand species.     

Analysis and parameter resolution in highly cooperative systems

We have examined common methods of analysis of highly cooperative systems such as oxygen binding by hemoglobin and thermal denaturation. Through extensive simulation of ligand-binding data for a tetrameric macromolecule we show that careful attention must be paid to the formulation of the fitting function and to proper assessment of the number of parameters involved. We conclude that the partition function should be formulated in terms of overall reaction parameters as opposed to stepwise reaction parameters and that bias is introduced by fixing physical parameters such as extrapolated end points.     

Looking inside molecular bonds at biological interfaces with dynamic force spectroscopy

Weak non-covalent interactions between large molecules govern interfacial structure and adhesion in biology. Because of thermal activation, these bonds have modest lifetimes and bond lifetimes are progressively shortened under application of external force. Theory predicts that bond survival time depends on how fast the force is applied and the expected survival time specifies the most likely breakage force (strength) at a given loading rate (force/time). Plotted as a function of log(e) (loading rate), the dynamic spectrum of bond strength provides an image of the prominent barriers traversed in the energy landscape along the unbinding pathway, which establishes a direct link between measurements of bond force and molecular-scale chemistry. Experimentally, the challenge is to measure bond strength over several orders of magnitude in loading rate. With a recently designed probe technique, we have measured strengths of single receptor-ligand bonds and receptor-membrane anchoring over an enormous range of loading rates from 10(-1) pN/s to 10(5) pN/s, which reveals an inner view of the complexity of these interactions.     

Physical properties of the specific PapG–galabiose binding in <Emphasis Type="Italic">E. coli</Emphasis> P pili-mediated adhesion

Detailed analyses of the mechanisms that mediate binding of the uropathogenic Escherichia coli to host cells are essential, as attachment is a prerequisite for the subsequent infection process. We explore, by means of force measuring optical tweezers, the interaction between the galabiose receptor and the adhesin PapG expressed by P pili on single bacterial cells. Two variants of dynamic force spectroscopy were applied based on constant and non-linear loading force. The specific PapG-galabiose binding showed typical slip-bond behaviour in the force interval (30-100 pN) set by the pilus intrinsic biomechanical properties. Moreover, it was found that the bond has a thermodynamic off-rate and a bond length of 2.6 x 10(-3) s(-1) and 5.0 A, respectively. Consequently, the PapG-galabiose complex is significantly stronger than the internal bonds in the P pilus structure that stabilizes the helical chain-like macromolecule. This finding suggests that the specific binding is strong enough to enable the P pili rod to unfold when subjected to strong shear forces in the urinary tract. The unfolding process of the P pili rod promotes the formation of strong multipili interaction, which is important for the bacterium to maintain attachment to the host cells.     

Force and compliance measurements on living cells using atomic force microscopy (AFM)

We describe the use of atomic force microscopy (AFM) in studies of cell adhesion and cell compliance. Our studies use the interaction between leukocyte function associated antigen-1 (LFA-1)/intercellular adhesion molecule-1 (ICAM-1) as a model system. The forces required to unbind a single LFA-1/ICAM-1 bond were measured at different loading rates. This data was used to determine the dynamic strength of the LFA-1/ICAM-1 complex and characterize the activation potential that this complex overcomes during its breakage. Force measurements acquired at the multiple- bond level provided insight about the mechanism of cell adhesion. In addition, the AFM was used as a microindenter to determine the mechanical properties of cells. The applications of these methods are described using data from a previous study. Published: January 15, 2004     

Dissociation kinetics of an enzyme-inhibitor system using single-molecule force measurements

We report on an improved method to interpret single molecule dissociation measurements using atomic force microscopy. We describe an easy to use methodology to reject nonspecific binding events, as well as estimating the number of multiple binding events. The method takes nonlinearities in the force profiles into account that result from the deformation of the used polymeric linkers. This new method is applied to a relevant enzyme-inhibitor system, latent matrix metalloprotease 9 (ProMMP-9, a gelatinase), and its inhibitor, tissue inhibitor of metalloproteases 1 (TIMP 1), which are important players in cancer metastasis. Our method provides a measured kinetic off-rate of 0.010 ± 0.003 s(-1) for the dissociation of ProMMP9 and TIMP1, which is consistent with values measured by ensemble methods.     

Life's Simple Measures: Unlocking the Proteome

Using modified nucleotides and selecting for slow off-rates in the SELEX procedure, we have evolved a special class of aptamers, called SOMAmers (slow off-rate modified aptamers), which bind tightly and specifically to proteins in body fluids. We use these in a novel assay that yields 1:1 complexes of the SOMAmers with their cognate proteins in body fluids. Measuring the SOMAmer concentrations of the resultant complexes reflects the concentration of the proteins in the fluids. This is simply done by hybridization to complementary sequences on solid supports, but it can also be done by any other DNA quantification technology (including NexGen sequencing). We use measurements of over 1000 proteins in under 100μL of serum or plasma to answer important medical questions, two of which are reviewed here. A number of bioinformatics methods have guided our discoveries, including principal component analysis. We use various methods to evaluate sample handling procedures in our clinical samples and can identify many parameters that corrupt proteomics analysis.     

Homeostatic non-shivering thermogenesis in humans facts and hypotheses

This review considers current research of different forms of non-shivering thermogenesis related to thermoregulatory and substrate homeostasis. The term “homeostatic non-shivering thermogenesis (HNST)” is proposed for explanation of facultative heat production stimulated by exposure to cold, food intake and accumulation of lactate during intensive muscle loading. Similarities and differences in physiological activity are displayed in three HNST types. Existence of a number of common points makes it possible to propose common physiological mechanisms of HNST realization. Among other candidates for HNST location, the brown adipose tissue (BAT) fits best as its function is specifi between thermogenic function in cold environment and diet-induced thermogenesis that makes it possible to link these two HNST types with BAT activity. Here we present the data indirectly confirming BAT functioning in processes of homeostatic normalization not related to cold acclimation or food intake. We also consider new data about BAT functional activity, its topographic body location, mechanisms of uncoupled respiration in different tissues in adult humans and about methods of BAT diagnostics which include the use of molecular markers. We list a number of facts confirming our suggestion about BAT activity being related to homeostatic normalization after physical loading. In conclusion, we propose an experimental research program for the testing of our hypothesis regarding BAT universal homeostatic function in humans.     

Multi-scale simulation of L-selectin–PSGL-1-dependent homotypic leukocyte binding and rupture

L-selectin–PSGL-1-mediated polymorphonuclear (PMN) leukocyte homotypic interactions potentiate the extent of PMN recruitment to endothelial sites of inflammation. Cell–cell adhesion is a complex phenomenon involving the interplay of bond kinetics and hydrodynamics. As a first step, a 3-D computational model based on the Immersed Boundary Method is developed to simulate adhesion-detachment of two PMN cells in quiescent conditions. Our simulations predict that the total number of bonds formed is dictated by the number of available receptors (PSGL-1) when ligands (L-selectin) are in excess, while the excess amount of ligands influences the rate of bond formation. Increasing equilibrium bond length results in a higher number of receptor–ligand bonds due to an increased intercellular contact area. On-rate constants determine the rate of bond formation, while off-rates control the average number of bonds by modulating bond lifetimes. Application of an external pulling force leads to time-dependent on- and off-rates and causes bond rupture. Moreover, the time required for bond rupture in response to an external force is inversely proportional to the applied load and decreases with increasing off-rate.     

Dynamic force spectroscopy of the digoxigenin-antibody complex

Small ligands and their receptors are widely used non-covalent couplers in various biotech applications. One prominent example, the digoxigenin-antibody complex, was often used to immobilize samples for single molecule force measurements by optical trap or AFM. Here, we employed dynamic AFM spectroscopy to demonstrate that a single digoxigenin-antibody bond is likely to fail even under moderate loading rates. This effect potentially could lower the yield of measurements or even obscure the unbinding data of the sample by the rupture events of the coupler. Immobilization by multiple antibody-antigen bonds, therefore, is highly recommended. The analysis of our data revealed a pronounced loading rate dependence of the rupture force, which we analyzed based on the well-established Bell-Evans-model with two subsequent unbinding barriers. We could show that the first barrier has a width of Deltax(1)=1.15 nm and a spontaneous rate of k(off1)=0.015 s(-1) and the second has a width of Deltax(2)=0.35 nm and a spontaneous rate of k(off2)=4.56 s(-1). In the crossover region between the two regimes, we found a marked discrepancy between the predicted bond rupture probability density and the measured rupture force histograms, which we discuss as non-Markovian contribution to the unbinding process.     

Maximum likelihood estimation of the kinetics of receptor-mediated adhesion

Adhesion flow assays are commonly employed to characterize the kinetics and force-dependence of receptor-ligand interactions. As transient cellular adhesion events are often mediated by a small number of receptor-ligand complexes (tether bonds) their durations are highly variable, which in turn presents obstacles to standard methods of analysis. In this paper, we employ the stochastic approach to chemical kinetics to construct the pause time distribution. Using this distribution, we develop a robust maximum likelihood (ML) approach to the robust estimation of rate constants associated with receptor-mediated transient adhesion and their confidence intervals. We then formulate robust estimators of the parameters of models for the force-dependence of the off-rate. Lastly, we develop a robust method of elucidation of the force-dependence of the off-rate using Akaike's information criterion (AIC). Our findings conclusively demonstrate that ML estimators of adhesion kinetics are substantial improvements over more conventional approaches, and when combined with Fisher information, they may be used to objectively and reproducibly distinguish the kinetics of different receptor-ligand complexes. Software for the implementation of these methods with experimental data is publicly available as for download at http://www.laurenzi.net.     

Microarray segmentation methods significantly influence data precision

Little consideration has been given to the effect of different segmentation methods on the variability of data derived from microarray images. Previous work has suggested that the significant source of variability from microarray image analysis is from estimation of local background. In this study, we used Analysis of Variance (ANOVA) models to investigate the effect of methods of segmentation on the precision of measurements obtained from replicate microarray experiments. We used four different methods of spot segmentation (adaptive, fixed circle, histogram and GenePix) to analyse a total number of 156 172 spots from 12 microarray experiments. Using a two-way ANOVA model and the coefficient of repeatability, we show that the method of segmentation significantly affects the precision of the microarray data. The histogram method gave the lowest variability across replicate spots compared to other methods, and had the lowest pixel-to-pixel variability within spots. This effect on precision was independent of background subtraction. We show that these findings have direct, practical implications as the variability in precision between the four methods resulted in different numbers of genes being identified as differentially expressed. Segmentation method is an important source of variability in microarray data that directly affects precision and the identification of differentially expressed genes.     

Computer simulation of rapidly responding forced exponential systems

Two common problems in computer simulations are the decisions to ignore or include a particular element of a system under study in a model and the choice of an appropriate integration algorithm. To examine aspects of these problems, a simple exponential system is considered in which a large simulation error is induced by a rather small truncation error. The effect of computational precision, step size and hardware selection on this error is examined at standard and extended precisions over a range of step sizes and on a variety of computers. For this model, simulation accuracy is an exponential function of the number of bits in the mantissa of the computer word. Optimal step size is a function of accuracy required and precision used; a trade-off between truncation and round-off errors becomes important as accuracy requirements increase. Machine selection is important primarily in economic terms if the required precision is available. We conclude that the effect on a simulation of small terms such as truncation errors can be unexpectedly large, that solutions should always be checked, and that high precision and wide dynamic range are important to the successful computer simulation of models such as that examined.     

Blind source separation methods for deconvolution of complex signals in cancer biology

Two blind source separation methods (Independent Component Analysis and Non-negative Matrix Factorization), developed initially for signal processing in engineering, found recently a number of applications in analysis of large-scale data in molecular biology. In this short review, we present the common idea behind these methods, describe ways of implementing and applying them and point out to the advantages compared to more traditional statistical approaches. We focus more specifically on the analysis of gene expression in cancer. The review is finalized by listing available software implementations for the methods described.     

Comparing the precision,accuracy, and efficiency of branch clipping and sweep netting for sampling arthropods in two Jamaican forest types

ABSTRACT Devising methods for sampling arthropods presents many challenges, including understanding possible differences in results obtained by different individuals (precision), investigating differences between estimates and the actual variable of interest (accuracy), and assessing the effort and cost of a given method (efficiency). We assessed the precision, accuracy, and efficiency of sweep netting and branch clipping, two common methods of sampling arthropods, in mangrove and second‐growth scrub forests in Jamaica, West Indies, in 2009. Three individuals used both methods sequentially to sample arthropods in the territories of American Redstarts (Setophaga ruticilla). We found that both branch clipping and sweep netting lacked precision because different individuals produced different estimates of either arthropod abundance (number of individuals per sample) or biomass. In both forests, more arthropods were sampled with sweep netting, in terms of biomass and abundance, and several orders of arthropods were collected that were missed by branch clipping. We also detected the absence of a predictable habitat‐based difference in arthropod biomass with sweep netting, but not with branch clipping. Sweep netting took longer overall (field and processing time combined) and was therefore less efficient. Despite problems with precision and efficiency, our results suggest that sweep netting may be a more accurate method than branch clipping for sampling foliage arthropods in some forest habitats. Our study also reveals the importance of recognizing and controlling for individual bias and of choosing arthropod sampling methods most appropriate to each study species and habitat type.